Geodesic
Coding knots by $T$-graphs
Contemporary Mathematics. Fundamental Directions, Algebra, Geometry, and Topology, Tome 66 (2020) no. 4, pp. 531-543

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In this paper, knots are considered as smooth embeddings of a circle into $\mathbb R^3$ defined by their flat diagrams. We propose a new method of coding knots by $T$-graphs describing the torsion structure on a flat diagram. For this method of coding, we introduce conceptions of a cycle and a block and describe transformations of $T$-graphs under the first and the third Reidemeister moves applied to the flat diagram of a knot. 
@article{CMFD_2020_66_4_a0,
     author = {O. N. Biryukov},
     title = {Coding knots by $T$-graphs},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {531--543},
     publisher = {mathdoc},
     volume = {66},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2020_66_4_a0/}
}
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O. N. Biryukov. Coding knots by $T$-graphs. Contemporary Mathematics. Fundamental Directions, Algebra, Geometry, and Topology, Tome 66 (2020) no. 4, pp. 531-543. http://geodesic.mathdoc.fr/item/CMFD_2020_66_4_a0/